Spherical harmonics decomposition and reproduction of a low frequency sound field within a cylindrical cavity

An efficient method for the spherical harmonics decomposition of a low frequency sound field within a cylindrical cavity using a movable space domain Spherical Microphone Array (SMA) was proposed. By measuring over different positions with the SMA, the sound field coefficients in the spherical harmonics domain with respective to the global origin can be effectively solved under the Compressive Sensing (CS) framework by only one time calculation. Firstly, the column coherence of the sensing matrix was discussed by comparing different configurations of SMA, the number of sampling points, different truncated orders as well as the measurement positions. The proposed method was then validated through an experiment conducted within an aircraft cabin mock-up, and compared with the conventional coordinate translations method. Sound pressures inside the cabin can be well reproduced by the proposed method with a rigid SMA consisting of 10 randomly selected sampling points measured over 3 positions, and higher accuracy of reproduced field can be achieved, meanwhile the computational efficiency has also been greatly improved.